Project plans are created to visualize and store data describing stages of design, implementation and manufacturing of future products and processes. A typical example is a several month long product development plan consisting of several hundred tasks performed by several dozen people. Even for this relatively moderate size project, creating a low-risk plan with consistent delivery on project milestones is a difficult problem, especially if the plan includes engineering, marketing, manufacturing, sales and support tasks, often executed at different geographical locations. For complex industrial projects (for example, multi-thousand task aircraft manufacturer projects), development of a consistent plan and schedule and its successful execution becomes extremely challenging because of a large number of project tasks and diversity of their attributes: duration, sequence, multiple predecessors and followers, resource sharing etc.
Small projects consisting of several tasks could be handled manually and may not even need detailed documentation. However, when the plan complexity increases manual planning becomes risky and inefficient. To reduce risk, wide variety of software packages is used for managing project data. A typical generic package is Microsoft Project. For more specialized applications, multiple packages are developed improving planning and scheduling in specific industries (a typical example is Primavera Project Planner), and a number of patents are issued suitable for specific types of processes and enterprises. For example, U.S. Pat. No. 6,609,100 [L. E. Smith and E. W. Balunas, Program Planning Management System] describes development of complex plans in aerospace industry by sorting and grouping of tasks between a database and a scheduler under user control. U.S. Pat. No. 6,873,961 B1 by S. W. Thorpe and R. C. Higgins describes method and apparatus for identifying and tracking military project trends in real time. Artificial Intelligence (AI) approaches intended for military and intelligent applications establish balance between the human and computer authority in the planning, scheduling and execution processes. A typical example is PASSAT [Myers, K. L., et al., PASSAT: A User-centric Planning Framework, in Proceedings of the Third International NASA Workshop on Planning and Scheduling for Space, 2002], organized around a library of templates encoding and prioritizing sub-plans and tasks around their commitments, previous experience, important knowledge etc. Model studies show AI tools may substantially improve time required to generate the plan, number of interactions between planners and schedulers, etc. [Myers, K. L. et al., Integrating Planning and Scheduling through Adaptation of Resource Intensity Estimates. Proceedings of the 6th European Conference on Planning (ECP-01), 2001].
Another approaches to improve planning and scheduling is analytical evaluation of plan risk based on mathematical tools. If the probability distribution is defined for each task, the milestone and the full project probability may be also defined. For example, if the milestone includes two individual tasks with durations y1 and y2 and dispersions σ1 and σ2, respectively, then the dispersion of the milestone Σ is defined by a relation:Σ2(y1+y2)=σ12+σ22±2ρ12σ1σ2  (1)where ρ12 is the mutual correlation coefficient. For independent tasks, ρ12=0. Similar relations may be applied to the milestones including more than two tasks. With the probability distribution known for each task, the probability of performing any milestone and the whole project may be calculated. To overcome analytical difficulties caused by multi-path correlations Monte Carlo computer simulations were developed. Respective programs are available commercially [http://www.cbpredictor.com/cases/caseindex.html, http://www.psteering.com/home/home.cfm], but for large projects they are not very efficient: even moderate task dispersion may result in very broad probability distributions. In a simple case where a milestone is comprised of 100 consecutive independent tasks of equal duration D, each duration being defined with 10% accuracy, the milestone probability distribution has dispersion equal to the task duration:√{square root over (Σ2(y1+y2+ . . . +y100))}=0.1D√{square root over (100)}=D  (2)To improve the resolution, each task could be further subdivided into sub-tasks; if the number of sub-tasks is 100; the milestone dispersion is decreased by √{square root over (100)}=10 times, according to conventional rules for random processes. Thus, milestone dispersion improves slowly, and the effort to define the detailed task structure might exceed the effort to perform the task. In practice, even 10% accuracy for the task duration may be difficult to achieve. For large projects consisting of hundreds and thousands of tasks and dozens of milestones, improvement of the task duration tolerances by sub-dividing into sub-tasks is unrealistic.
Therefore new approaches are needed to increase confidence in planning and execution and improve ability to evaluate plan quality from entirely structural point of view, unrelated to the industry specifics.